Using eig

Consider the complex matrix

r $=$ RandStream$(\text{'}$mt$19937$ar$\text{'},$'Seed',$1234)$;

A $=$ r$.$randn$(10,10)+1$i$*$r$.$randn$(10,10)$; $($here i represents the unit imaginary number$)$

Using the eig command in MATLAB, compute the matrices V and D such that A $=$ V$*$D$*$inv$($V$).$ Recall the the first column of V corresponds to the first eigenvalue D$(1,1).$ The second column of V corresponds to the second eigenvalue D$(2,2),$ and so on$.$

Reorder the diagonal entries of D so that the real part is increasing down the diagonal $($it may be useful to use the real and imag commands on MATLAB$).$ Reorder the columns of V accordingly so that A $=$ V$*$D$*$inv$($V$)$ still holds $($check this!$).$ Then save:

The real part of V as A$7$

The imaginary part of V as A$8$

The real part of D as A$9$

The imaginary part of D as A$10$